The Monty Hall Problem: Should You Switch?

The Monty Hall problem is one of the most famous probability puzzles. You pick door 1. Monty, who knows where the car is, opens door 3 (a goat). Should you switch to door 2?

Yes! Switching wins 2/3 of the time. When you first picked, you had a 1/3 chance of being right. That means the car is behind one of the other doors with probability 2/3. When Monty eliminates one wrong door, all 2/3 probability concentrates on the remaining door.

This is counterintuitive because people think "two doors left, so it is 50/50." But your original choice was made from 3 doors — that prior information matters.